Advances in experimental protocols, in particular at the sub-cellular level, and in computational modeling of organ physiology, like the heart for instance, enable the investigation of functional relationships between sub-cellular mechanisms and organ function. For example, the output of detailed sub-cellular models that describe the molecular pathways involved in cardiac myocyte function may be linked to a multi-scale, continuum framework to compute the impact of these pathways at an organ level. However, such detailed models typically rely on numerous algebraic or ordinary differential equations, which may span several temporal and spatial scales. Consequently, these models are computationally demanding and are controlled by a large number of parameters whose direct influence at the organ level, where clinical observations are usually available, is not easily observable. For these reasons, it is challenging to personalize these models, for example, to specific genetic groups, populations, or individual patients.
Various model reduction techniques that rely on statistical learning have been investigated, in particular in the chemometrics community. Often referred to as meta-modeling, these techniques aim to derive a statistical model that is able to capture the output of complex, non-linear computational models while being expressed with fewer parameters. Such models have been used not only to analyze the interactions between parameters, but also to estimate the parameters using libraries of models. Additionally, in the computer vision and medical imaging domain, manifold learning techniques have been applied to reduce the dimensionality of multi-dimensional spaces so that the corresponding data can be visualized. However, these techniques conventionally have been limited to their respective domains and have not been combined, or otherwise extended, to address the challenges of computational complexity and personalization that are associated with modeling heart function. In particular, they have not been applied so far to reduce the complexity of a known multi-scale model.
Accordingly, it is desired to develop a model reduction strategy that may be applied to multi-scale cardiac modeling to reduce the number of parameters of such models and to learn data-driven generative models suitable for simulations which capture the output of their original, corresponding multi-scale models. Such a model would allow fast, patient-specific multi-scale computation.